Below are listed rank-two temperaments supported by the 15edo patent val, below the indicated cutoff in TE badness.

7-limit temperaments with badness below 0.06

Listed is the wedgie and the TE badness times 1000 for 15 temperaments with badness less than 0.06.

Rank	Wedgie	Name	Badness	Commas
1	<<3 0 -6 -7 -18 -14]]	Augene	24.816	64/63 126/125
2	<<0 5 0 8 0 -14]]	Blacksmith	25.640	28/27 49/48
3	<<6 5 3 -6 -12 -7]]	Keemun	27.408	49/48 126/125
4	<<9 5 -3 -13 -30 -21]]	Valentine	31.056	126/125 1029/1024
5	<<3 5 9 1 6 7]]	Opossum	40.650	28/27 126/125
6	<<3 5 -6 1 -18 -28]]	Porcupine	41.057	64/63 250/243
7	<<21 15 -12 -25 -78 -70]]	Nessafof	45.048	6144/6125 250047/250000
8	<<39 30 -18 -43 -138 -126]]	Pnict	45.660	250047/250000 2100875/2097152
9	<<9 10 -3 -5 -30 -35]]	Superkleismic	47.932	875/864 1029/1024
10	<<12 10 -9 -12 -48 -49]]	Hemikleismic	52.054	4000/3969 6144/6125
11	<<3 0 9 -7 6 21]]	Inflated	54.729	28/27 128/125
12	<<6 0 3 -14 -12 7]]	Triforce	54.988	49/48 128/125
13	<<18 15 -6 -18 -60 -56]]	Tritikleismic	56.337	1029/1024 15625/15552
14	<<6 10 3 2 -12 -21]]	Nautilus	57.420	49/48 250/243
15	<<60 45 -30 -68 -216 -196]]		58.002	250047/250000 12884901888/12867859375

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE badness times 1000 for 33 temperaments with badness less than 0.05.

Rank	Wedgie	Name	Badness	Commas
1	<<9 5 -3 7 -13 -30 -20 -21 -1 30]]	Valentine	16.687	121/120 126/125 176/175
2	<<18 15 -6 9 -18 -60 -48 -56 -31 46]]	Tritikleismic	19.333	385/384 441/440 4000/3993
3	<<3 0 -6 -6 -7 -18 -20 -14 -14 4]]	Augene	19.613	56/55 64/63 100/99
4	<<3 5 -6 4 1 -18 -4 -28 -8 32]]	Porcupine	21.562	55/54 64/63 100/99
5	<<3 5 9 4 1 6 -4 7 -8 -20]]	Opossum	22.325	28/27 55/54 77/75
6	<<0 5 0 -5 8 0 -8 -14 -29 -14]]	Blacksmith	24.641	28/27 49/48 55/54
7	<<9 10 -3 2 -5 -30 -28 -35 -30 16]]	Superkleismic	25.659	100/99 245/242 385/384
8	<<6 10 3 8 2 -12 -8 -21 -16 12]]	Nautilus	26.023	49/48 55/54 100/99
9	<<6 0 3 3 -14 -12 -16 7 7 -2]]	Triforce	26.152	49/48 56/55 77/75
10	<<6 5 3 -2 -6 -12 -24 -7 -22 -16]]	Keemun	27.41	49/48 56/55 100/99
11	<<6 5 3 13 -6 -12 0 -7 13 26]]	Darjeeling	27.648	49/48 55/54 77/75
12	<<0 5 0 10 8 0 16 -14 6 28]]	Ferrier	29.2	28/27 49/48 77/75
13	<<3 -5 -6 -1 -15 -18 -12 0 15 18]]	Progress	31.036	56/55 64/63 77/75
14	<<3 0 9 9 -7 6 4 21 21 -6]]	Inflated	31.171	28/27 55/54 128/125
15	<<12 5 -9 1 -20 -48 -40 -35 -15 34]]	Thuja	33.078	126/125 176/175 1344/1331
16	<<27 20 -9 16 -31 -90 -68 -77 -32 76]]	Tritriple	35.350	385/384 441/440 43923/43750
17	<<3 0 -6 9 -7 -18 4 -14 21 46]]		35.554	55/54 64/63 77/75
18	<<6 5 -12 -2 -6 -36 -24 -42 -22 36]]		36.894	64/63 100/99 1331/1323
19	<<12 10 -9 11 -12 -48 -24 -49 -9 62]]		38.230	121/120 176/175 4000/3969
20	<<12 10 6 11 -12 -24 -24 -14 -9 10]]		42.696	49/48 121/120 126/125
21	<<3 10 9 14 9 6 12 -7 -2 8]]		43.195	28/27 77/75 245/242
22	<<15 10 -15 5 -19 -66 -44 -63 -23 66]]		43.508	176/175 1331/1323 4000/3969
23	<<33 25 -21 14 -37 -126 -92 -119 -54 112]]		43.743	3025/3024 4000/3993 6144/6125
24	<<15 15 0 15 -11 -42 -28 -42 -17 42]]		44.405	121/120 441/440 875/864
25	<<6 0 -12 3 -14 -36 -16 -28 7 50]]		44.448	64/63 121/120 126/125
26	<<15 10 0 5 -19 -42 -44 -28 -23 14]]		45.070	126/125 245/242 385/384
27	<<0 10 0 5 16 0 8 -28 -23 14]]		45.972	28/27 49/48 121/120
28	<<30 20 -15 10 -38 -108 -88 -91 -46 80]]		47.990	441/440 4000/3993 6144/6125
29	<<9 0 -3 -3 -21 -30 -36 -7 -7 2]]		48.345	56/55 128/125 2541/2500
30	<<3 0 9 -6 -7 6 -20 21 -14 -48]]		48.744	28/27 77/75 128/125
31	<<21 15 -12 3 -25 -78 -68 -70 -45 50]]		48.836	441/440 1344/1331 4375/4356
32	<<0 5 15 10 8 24 16 21 6 -24]]		49.486	56/55 100/99 256/243
33	<<3 10 -6 -1 9 -18 -12 -42 -37 18]]		49.863	55/54 64/63 245/242

13-limit temperaments with badness below 0.04

Listed is the wedgie and the TE badness times 1000 for 59 temperaments with badness less than 0.04.

Rank	Wedgie	Name	Badness	Commas
1	<<18 15 -6 9 42 -18 -60 -48 0 -56 -31 42 46 140 112]]	Tritikleismic	15.652	325/324 364/363 441/440 625/624
2	<<3 5 9 4 2 1 6 -4 -8 7 -8 -14 -20 -28 -8]]	Opossum	19.389	28/27 40/39 55/54 66/65
3	<<6 0 3 3 9 -14 -12 -16 -8 7 7 21 -2 14 20]]	Triforce	20.248	49/48 56/55 66/65 77/75
4	<<0 5 0 -5 5 8 0 -8 8 -14 -29 -7 -14 14 36]]	Blacksmith	20.498	28/27 40/39 49/48 55/54
5	<<3 0 -6 -6 -3 -7 -18 -20 -16 -14 -14 -7 4 14 12]]	Augene	20.785	40/39 56/55 64/63 66/65
6	<<3 5 -6 4 2 1 -18 -4 -8 -28 -8 -14 32 28 -8]]	Porcupine	21.276	40/39 55/54 64/63 66/65
7	<<9 5 -3 7 11 -13 -30 -20 -16 -21 -1 7 30 42 12]]	Lupercalia	21.328	66/65 105/104 121/120 126/125
8	<<6 5 3 13 14 -6 -12 0 0 -7 13 14 26 28 0]]		21.445	49/48 55/54 66/65 77/75
9	<<9 10 -3 2 16 -5 -30 -28 -8 -35 -30 0 16 56 48]]	Superkleismic	21.478	100/99 105/104 245/242 1188/1183
10	<<6 10 3 8 19 2 -12 -8 8 -21 -16 7 12 42 36]]	Nautilus	22.285	49/48 55/54 91/90 100/99
11	<<0 5 0 10 5 8 0 16 8 -14 6 -7 28 14 -20]]		22.325	28/27 40/39 49/48 66/65
12	<<6 5 3 -2 14 -6 -12 -24 0 -7 -22 14 -16 28 56]]	Keema	22.749	49/48 56/55 91/90 625/624
13	<<12 5 -9 1 23 -20 -48 -40 -8 -35 -15 35 34 98 76]]	Thuja	22.838	126/125 144/143 176/175 364/363
14	<<3 0 -6 -6 12 -7 -18 -20 8 -14 -14 28 4 56 64]]		22.890	56/55 64/63 91/90 100/99
15	<<9 5 -3 7 26 -13 -30 -20 8 -21 -1 42 30 84 64]]	Dwynwen	23.461	91/90 121/120 126/125 176/175
16	<<3 5 -6 4 17 1 -18 -4 16 -28 -8 21 32 70 44]]	Porcupinefish	25.314	55/54 64/63 91/90 100/99
17	<<12 10 -9 11 28 -12 -48 -24 0 -49 -9 28 62 112 56]]	Hemikleismic	26.005	121/120 176/175 275/273 325/324
18	<<3 -5 -6 -1 7 -15 -18 -12 0 0 15 35 18 42 28]]	Progress	26.214	56/55 64/63 66/65 77/75
19	<<6 5 -12 -2 14 -6 -36 -24 0 -42 -22 14 36 84 56]]		26.336	64/63 100/99 144/143 275/273
20	<<3 0 9 9 12 -7 6 4 8 21 21 28 -6 0 8]]		28.940	28/27 55/54 66/65 147/143
21	<<0 0 0 0 15 0 0 0 24 0 0 35 0 42 52]]		28.944	28/27 49/48 55/54 77/75
22	<<3 0 9 9 -3 -7 6 4 -16 21 21 -7 -6 -42 -44]]		29.443	28/27 40/39 55/54 245/242
23	<<3 5 9 4 17 1 6 -4 16 7 -8 21 -20 14 44]]		29.806	28/27 55/54 77/75 105/104
24	<<6 10 3 8 4 2 -12 -8 -16 -21 -16 -28 12 0 -16]]		29.816	40/39 49/48 55/54 66/65
25	<<30 20 -15 10 65 -38 -108 -88 -8 -91 -46 77 80 238 188]]		29.837	364/363 441/440 676/675 40824/40625
26	<<3 0 -6 9 12 -7 -18 4 8 -14 21 28 46 56 8]]		29.922	55/54 64/63 66/65 77/75
27	<<27 20 -9 16 53 -31 -90 -68 -16 -77 -32 49 76 182 124]]		30.930	385/384 441/440 625/624 1188/1183
28	<<6 5 3 -2 -1 -6 -12 -24 -24 -7 -22 -21 -16 -14 4]]		31.633	40/39 49/48 56/55 66/65
29	<<3 -5 -6 -1 -8 -15 -18 -12 -24 0 15 0 18 0 -24]]		32.217	40/39 56/55 64/63 77/75
30	<<0 5 0 -5 -10 8 0 -8 -16 -14 -29 -42 -14 -28 -16]]		32.301	28/27 49/48 55/54 66/65
31	<<15 15 0 15 30 -11 -42 -28 -8 -42 -17 14 42 84 48]]		32.378	105/104 121/120 275/273 325/324
32	<<6 0 -12 3 9 -14 -36 -16 -8 -28 7 21 50 70 20]]		32.379	64/63 66/65 121/120 676/675
33	<<3 10 9 14 7 9 6 12 0 -7 -2 -21 8 -14 -28]]		32.653	28/27 40/39 77/75 147/143
34	<<12 10 6 11 28 -12 -24 -24 0 -14 -9 28 10 56 56]]		32.900	49/48 91/90 121/120 126/125
35	<<15 10 0 5 25 -19 -42 -44 -16 -28 -23 21 14 70 68]]		33.410	105/104 126/125 144/143 245/242
36	<<3 0 -6 9 -3 -7 -18 4 -16 -14 21 -7 46 14 -44]]		33.779	40/39 55/54 64/63 77/75
37	<<18 10 -6 14 37 -26 -60 -40 -8 -42 -2 49 60 126 76]]		34.916	121/120 126/125 176/175 676/675
38	<<0 10 0 5 10 16 0 8 16 -28 -23 -14 14 28 16]]		35.251	28/27 40/39 49/48 121/117
39	<<30 25 -15 20 70 -30 -108 -72 0 -105 -40 70 108 252 168]]		35.285	325/324 385/384 625/624 1331/1323
40	<<9 10 -3 2 31 -5 -30 -28 16 -35 -30 35 16 98 100]]		36.091	91/90 100/99 245/242 625/624
41	<<0 5 15 10 5 8 24 16 8 21 6 -7 -24 -42 -20]]		36.155	40/39 56/55 66/65 256/243
42	<<3 10 -6 -1 7 9 -18 -12 0 -42 -37 -21 18 42 28]]		36.463	40/39 55/54 64/63 245/242
43	<<0 0 0 15 0 0 0 24 0 0 35 0 42 0 -56]]		36.794	28/27 40/39 49/48 126/125
44	<<6 5 3 13 -1 -6 -12 0 -24 -7 13 -21 26 -14 -52]]		36.933	40/39 55/54 77/75 147/143
45	<<3 5 -6 -11 2 1 -18 -28 -8 -28 -43 -14 -10 28 48]]		37.036	40/39 56/55 64/63 250/243
46	<<21 15 -12 3 39 -25 -78 -68 -16 -70 -45 35 50 154 124]]		37.409	144/143 364/363 441/440 625/624
47	<<3 10 9 -1 7 9 6 -12 0 -7 -37 -21 -34 -14 28]]		37.431	28/27 40/39 55/54 539/507
48	<<21 20 -12 13 44 -17 -78 -52 -8 -84 -39 28 78 168 104]]		37.468	275/273 325/324 385/384 1331/1323
49	<<3 0 9 -6 -3 -7 6 -20 -16 21 -14 -7 -48 -42 12]]		37.500	28/27 40/39 66/65 385/384
50	<<6 0 3 3 -6 -14 -12 -16 -32 7 7 -14 -2 -28 -32]]		37.775	40/39 49/48 56/55 121/117
51	<<12 10 -9 -4 28 -12 -48 -48 0 -49 -44 28 20 112 112]]		37.792	100/99 144/143 245/242 625/624
52	<<15 10 -15 5 40 -19 -66 -44 8 -63 -23 56 66 168 120]]		38.006	176/175 325/324 364/363 640/637
53	<<12 15 -9 6 33 -4 -48 -32 8 -63 -38 21 48 126 92]]		38.228	100/99 275/273 385/384 572/567
54	<<9 0 -3 -3 6 -21 -30 -36 -24 -7 -7 14 2 28 32]]		38.535	56/55 66/65 105/104 637/625
55	<<24 15 -18 12 51 -32 -96 -64 -8 -84 -24 63 96 210 132]]		38.616	176/175 640/637 676/675 1331/1323
56	<<24 20 -18 7 56 -24 -96 -72 0 -98 -53 56 82 224 168]]		38.844	325/324 364/363 625/624 640/637
57	<<0 0 15 0 0 0 24 0 0 35 0 0 -52 -56 0]]		38.991	40/39 55/54 66/65 256/243
58	<<33 25 -21 14 67 -37 -126 -92 -16 -119 -54 63 112 266 180]]		39.	625/624 640/637 1188/1183 1575/1573
59	<<9 10 12 17 16 -5 -6 -4 -8 0 5 0 6 0 -8]]		39.006	55/54 66/65 77/75 147/143